Fictitious Statistical Study (Research Paper Sample)

Fictitious Statistical Study Name: Subject: Date of Submission: Fictitious Statistical Study Introduction According to Acham, Kikafunda, Oluka, Malde, Tylleskar (2008), cases of obesity and overweight are associated with increased risk for diseases such as heart disease especially when body fat is deposited in the abdomen. This owes to the reality that individuals with huge fat deposits in the abdomen always have large waist circumferences. It is notable that the emergence of cases of obesity and overweight forced scholars to develop a tool for measuring an individual's fat content in relation to the individual's height. Specifically, scholars developed the body mass index, which measures an individual's weight with relation to the individual's height. It is important to understand how the body mass index is calculated because the upcoming discussion is focused on body mass index. It follows that the body mass index (BMI) is obtained after dividing an individual's weight in kilograms by the individual's height in meters. It is crucial to highlight that studies have been conducted on the acceptable standards of body mass index. As evidenced, World Health Organization (2004) argues that a study conducted in Asia, Europe, and North America reveals that a body mass index of 21Kg/M2 and above is associated with high risks of cardiovascular diseases. This owes to the reality that individuals with such BMIs are at high risks of contracting diseases such as ischaemic heart disease, type II diabetes, ischaemic stroke, hypertensive diseases, and osteoarthritis. Critical to the discussion is the fact that a different study reveals that the global burden of diseases associated with high BMIs amounts to 30 million disabilities that were adjusted for life years in 2000 (Bogin and Varela-Silva, 2012). Researchers have also used the current trend and have predicted an increase in diseases associated with high BMIs if no measures are taken. In a different study, Kitahara, Gamborg, Pretha, Sorensen, and Baker, (2014) examined the effect of height and weight at birth. The authors concluded that extreme high cases of BMI at birth increase the risk of developing glioma in adulthood. Evidently, BMI plays a crucial role in the health of the current society. Simply put, the global society should understand BMI because it plays a crucial role in the wellbeing of the society. It is important to highlight that studies reveal that the body mass index can be calculated based on an individual's weight and height (Franz and Feresu, 2013). Critical to the debate is the fact that different studies have examined BMI beyond height and weight. For instance, Sperrin, Marshall, Higgins, Rnehan, and Bucha (2015) argue that factors such as waist circumference, chest circumference, and waist circumference could be used to identify an individual's body mass index. This paper examines whether age, height, and weight have an influence on body mass index. Particularly, the paper describes observations for the variables mentioned above and uses the multivariate linear regression analysis technique to examine the effect of age, weight, and height on BMI. The results indicate that weight and height are significant predictors of BMI, but age cannot predict an individual's BMI. Methodology As mentioned above, the study intended to identify the effect of age, weight, and height on BMI. Therefore, it could be deduced that the researcher treated age, height, and weight as the independent variable and BMI as the response variable. Critical to the discussion is the fact the researcher formulated the hypothesis indicated below prior to beginning the study. Further, it is important to note that the data used was not collected from any population because the researcher simulated the data based on the relationship between height and weight. This owes to the reality that the researcher was interested in developing a model that could complement outcomes from previous studies. It is also important to note that the researcher used a data set with fifty observations. H0: Age, height, and weight have no effect on BMI H1: Age, height, and weight have an effect on BMI The simulated data was then cleaned in Microsoft Excel and analyzed in SPSS using descriptive statistics and multiple linear regression techniques. All regression diagnostics were checked to ensure that all the assumptions for linear regression were met. For instance, outliers were checked by plotting scatterplots for all the variables, with BMI as the dependent variable for all the plots. Any significant outliers were removed from the data, which resulted in the removal of two observations. Consequently, the researcher simulated two additional observations to ensure that the data met the desired population size of fifty observations. It is important to note that all data manipulation techniques were completed in Microsoft Excel before the data was analyzed in SPSS. Regression Diagnostics Regression analysis requires that the assumption of linearity be met for the outcome of the test to be credible. Specifically, the assumption requires that the relationship between the outcome variable and all predictor variables be linear. Consequently, the researcher checked to ensure that the relationship between BMI and all the independent variables is linear, which was done using a scatterplot of BMI and the independent variables. Critical to the discussion is the fact that all the independent variables had a linear relationship with BMI. The diagrams depicted in figure 1 below, indicate the presence of a linear relationship between BMI and the independent variables. Figure 1: Scatterplots used to check for a linear trend The assumption of normality of error terms must be ascertained to ensure that the forecasts, scientific insights, and confidence intervals yielded from the regression model are efficient. The assumption was checked using normal probability plots shown below. This was done by running the regression analysis and selecting the normality plots in SPSS. The results obtained from the test are depicted in in figure two below. From figure two, it is evident that all the observations fall within the normal line indicating that the normality of error terms is ascertained Figure 2: PP plots from regression analysis The independence of error terms were also checked to ensure that errors associated with a single observation were not related or similar to errors produced by another observation. This was completed by checking the collinearity diagnostics when running the regression analysis in SPSS. The results from the output are depicted in table one below, and prove that all the error terms were independent of one another. As evidenced, the results indicate very low correlation coefficients between variables, which imply the absence of correlation between the variables. This owes to the very low correlation co-efficient between the variables. Collinearity Diagnostics Model Dimension Eigenvalue Condition Index Variance Proportions (Constant) Age HeightMetres Weightkg 1 1 3.934 1.000 .00 .00 .00 .00 2 .051 8.792 .00 .76 .00 .06 3 .015 16.316 .02 .09 .01 .70 4 .000 90.445 .98 .15 .99 .23 a. Dependent Variable: BodyMassIndex Table 1: Collinearity diagnostics Ultimately, the homogeneity of variance was ensured by plotting a scatterplot of the dependent variable against the residuals. This was done by creating a plot with the dependent variable against the residuals. The results are depicted in figure three below, and demonstrate that the error terms have a constant variance. This owes to the reality that the points in the graph were evenly distributed below and above the trend line. Further, they were also randomly distributed (without a specific pattern). A correlational analysis was also conducted to identify any relationship between the predictor variables and the response variable. Justification for Using Multiple Linear Regression The regression diagnostics reveal that the test met the required conditions owing to the fact that the model met all the required assumptions. It is also crucial to highlight that the researcher was justified to use multiple linear regression analysis because of the variables present and the research problem. As Carver, and Nash (2011) reveals linear regression analysis (whether simple or multiple) is used to identify, the presence, nature, and type of the relationship between variables. The author further asserts that most of the variables must be continuous before regression analysis could be used. In this case, BMI, age, weight, and weight are continuous variables, which meet the one condition for using regression analysis. Verma (2013) further argues that in cases where a researcher is predicting a relationship between two or more independent variables, then multiple regression analysis should be used. Evidently, the researcher was justified to use multiple linear regression analysis because the required conditions for running the tests were met. Further, the researcher was examining a relationship between one dependent variable and three predictor variables. Results Descriptive Statistics As mentioned above, descriptive statistics were used to summarize the data prior to running the main test. Vital to the debate is the fact that the researcher used the minimum, the mean, the maximum, the variance, the range, and the standard deviation to describe the data. The descriptive statistics was possible by selecting analyze, then descriptives, and entering the variables BMI, age, weight, and height. The research...